Information on Result #1201236
Digital (65, 77, 2861738)-net over F64, using net defined by OOA based on linear OOA(6477, 2861738, F64, 15, 12) (dual of [(2861738, 15), 42925993, 13]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(6477, 5723477, F64, 3, 12) (dual of [(5723477, 3), 17170354, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6477, 5723478, F64, 3, 12) (dual of [(5723478, 3), 17170357, 13]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(6411, 131076, F64, 3, 4) (dual of [(131076, 3), 393217, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(6411, 262152, F64, 4) (dual of [262152, 262141, 5]-code), using
- construction X4 applied to Ce(3) ⊂ Ce(1) [i] based on
- linear OA(6410, 262144, F64, 4) (dual of [262144, 262134, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(644, 262144, F64, 2) (dual of [262144, 262140, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(647, 8, F64, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,64)), using
- dual of repetition code with length 8 [i]
- linear OA(641, 8, F64, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, 64, F64, 1) (dual of [64, 63, 2]-code), using
- Reed–Solomon code RS(63,64) [i]
- discarding factors / shortening the dual code based on linear OA(641, 64, F64, 1) (dual of [64, 63, 2]-code), using
- construction X4 applied to Ce(3) ⊂ Ce(1) [i] based on
- OA 2-folding and stacking [i] based on linear OA(6411, 262152, F64, 4) (dual of [262152, 262141, 5]-code), using
- linear OOA(6421, 2796201, F64, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6421, large, F64, 6) (dual of [large, large−21, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OOA 3-folding [i] based on linear OA(6421, large, F64, 6) (dual of [large, large−21, 7]-code), using
- linear OOA(6445, 2796201, F64, 3, 12) (dual of [(2796201, 3), 8388558, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6445, large, F64, 12) (dual of [large, large−45, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 3-folding [i] based on linear OA(6445, large, F64, 12) (dual of [large, large−45, 13]-code), using
- linear OOA(6411, 131076, F64, 3, 4) (dual of [(131076, 3), 393217, 5]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(6477, 5723478, F64, 3, 12) (dual of [(5723478, 3), 17170357, 13]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (142, 154, 5723476)-net over F8 | [i] | Trace Code for Nets | |